The present invention relates generally to fluid flow measurement methods and apparatus, and more particularly to a new method and apparatus for measuring the mass flow rate of fluids flowing through closed conduits using the Magnus Effect. In accordance with the invention, an oscillating probe is extended into a flow stream and experiences an oscillating Magnus xe2x80x9clift forcexe2x80x9d that relates to fluid mass flow rate.
Historically, the Magnus Effect and its more rigorous counterpart, the Kutta-Joukowski Theorem (xe2x80x9cKJTxe2x80x9d), have been used to describe the lift force experienced by a spinning cylinder immersed in a transversely flowing air stream. The KJT mathematically describes the phenomenon of lift resulting from fluid flowing around the object. Using the KJT, one can demonstrate that if an object such as a cylinder (sphere or other shaped object) 10 is placed in an air stream 12, as depicted in FIG. 1, no lift force results. However, rotating the cylinder 10 about its axis 13 as suggested by the arrow 14, and in the flowing stream 12 produces a lift force FL. The lift force experienced by the rotating cylinder is called the xe2x80x9cMagnus Effectxe2x80x9d in recognition of Heinrich Magnus, a German Physicist, who studied deviations in the trajectories of spinning artillery shells. It is now understood that the Magnus lift force explains why baseballs xe2x80x9ccurvexe2x80x9d, tennis balls xe2x80x9ccutxe2x80x9d, and golf balls xe2x80x9chookxe2x80x9d or xe2x80x9cslicexe2x80x9d. The KJT describes the lift force FL acting on a cylinder of length L, radius R, spinning at a rate of S revolutions per unit time about its longitudinal axis 13 as proportional, in part, to the product of fluid density and fluid velocity. According to the KJT, the lift force per unit length, FL, exerted on the spinning cylinder is:
xe2x80x83FL=xcfx81Vxcex93xe2x80x83xe2x80x83(1)
Where xcfx81=air density, V=free stream air velocity, and xcex93=the circulation of fluid around the object defined as the line-integral of the fluid velocity around the spinning cylinder""s circumference C:
xcex93=∫CVRdr=2xcfx80RVRxe2x80x83xe2x80x83(2)
VR is the fluid velocity at the periphery of the cylinder and, in this particular case, equals the cylinder""s peripheral surface velocity because the fluid boundary layer adheres to the cylinder""s surface. VR=2xcfx80RS, is the velocity of the rotating cylinder at its periphery with S being the rate at which the cylinder spins. The direction of the lift force is perpendicular to both the cylinder""s longitudinal axis and the direction of the fluid velocity V as depicted in FIG. 1. The Magnus lift force is distributed along the portion of the cylinder""s length exposed to the fluid stream. Equation (1) applies to a surface of any cross-sectional shape regardless of whether the circulation, xcex93, is xe2x80x9cmechanically inducedxe2x80x9d (as with rotating a cylinder), xe2x80x9cnaturalxe2x80x9d (as with an airfoil), or a combination thereof.
Classically, the Magnus Effect applies only to mechanically induced circulation of fluid around an object (but not necessarily cylindrical in shape). Mechanically induced circulation causes the boundary layer adhering to the cylinder""s surface to interact with the flowing stream resulting in a momentum transfer from the free-stream flow, across the boundary layer, to the cylinder. This momentum transfer causes the rotating object to experience a lift force directly proportional to the momentum of the fluid stream. The mass flow rate, QM, of a fluid of density, xcfx81, flowing with average velocity, V, through a conduit of cross sectional area, Ac, is:
QM=xcfx81VAcxe2x80x83xe2x80x83(3)
The ability to measure a fluid""s rate of mass flow using the Magnus Effect is based partially on the fact that, the magnitude of the Magnus lift force, like the fluid mass flow rate, QM, is proportional to xcfx81V.
Others in the field have recognized the potential applicability of this technique to the measurement of mass flow rate. For example, in the Japanese Application Number JP1990000128718 of OGAWA YUTAKA and KAWAOTO HIROSHI with Issued/Filed Dates of Jan. 27, 1992/May 17, 1990, the applicants disclose that they believe they can measure mass flow rate by using a strain gage to determine the Magnus dynamic lift on a cylinder rotating at constant speed in a viscous fluid. The Magnus dynamic xe2x80x9cliftxe2x80x9d is measured as a function of the change of the strain of strain gages, and the change in the strain quantity is converted to an electrical signal by a bridge circuit to provide a value proportional to the geometric product of the flow velocity and the density. This information is then used to determine mass flow rate.
In a second Japanese Application Number JP1992000101875, bearing Issued/Filed Dates of Oct. 22, 1993/Mar. 29, 1992, to INA YOSHITAKA, NAKAO SHINICHI and HAYAKAWA MASAO, the mass flow rate of a gas flow running at a fixed velocity V through a passage is measured by a rotary cylinder disposed in the gas passage and rotated at a fixed peripheral velocity. Pressures P1 and P2 generated on opposite sides of the outer periphery of the rotary cylinder by this rotation are supplied to a differential pressure detector and the differential pressure between the sensors is determined. Based on this differential pressure, the mass flow rate Qm is determined using the relationship of P=2Qm(v/A).
Both of these references require that rotation of the cylinder be kept constant; that is, they require rotating a drive motor at constant rotating speed. The second reference also requires that pressures P1 and P2 generated in the vicinity of the xe2x80x9cupper and lower placesxe2x80x9d of the outer periphery of the rotary cylinder be measured to determine mass flow rate. These approaches have certain disadvantages. For example, the need to rotate the cylinder at constant speed requires closed-loop feedback and control of motor speed, which adds expense. Not having adequate motor speed control is a serious limitation, in that any variation in motor speed will directly result in a mass flow measurement error.
Another disadvantage is that these approaches require sealing of the xe2x80x9ccylinderxe2x80x9d, or its connecting shaft, from the fluid, and from the cylinder""s drive motor and the xe2x80x9coutside worldxe2x80x9d. This type of construction imposes multiple problems that affect performance, reliability, and usage/application. Sliding seals or gaskets exhibit a pressure sensitivity that can exert forces on the probe, which can compete with the Magnus force, thereby producing mass flow measurement errors. This is especially important in that many industrial applications experience flow pulsation due to fans, compressors, and pumps. Sliding seals can also present fluid compatibility problems with highly corrosive fluids, and/or safety problems related to the reliable sealing or escapement of toxic or volatile fluids. Also, seals require maintenance, and impose pressure-rating limitations. Sliding seals also exert friction on motor parts that can influence motor speed control. Because seals must by their nature be compliant, they necessarily xe2x80x9cabsorbxe2x80x9d some of the cylinder""s Magnus force deflection and thereby further limit the ability of the apparatus to measure lower mass flow rates accurately, particularly in the case of gases.
A further disadvantage is that strain gauges have limited usefulness because they must be bonded securely and permanently to the cylinder shaft. The integrity of the bond can degrade with temperature, thereby restricting the useful operating temperature range. Moreover, pulsations and vibrations coupling into the cylinder from the pipe and fluid can introduce periodic and random signals into the strain gauges that can be misinterpreted as being xe2x80x9crealxe2x80x9d and related to mass flow.
Still another problem associated with the Japanese inventors"" approaches is that they require pressure sensing. This can restrict the useful measurement range at low differential pressures. It also adds cost and more complexity to the device. Pressure sensing will have difficulty with pressure pulsations creating large common-mode pressures that can restrict application and usefulness of the device as well as contribute to further mass flow measurement errors. Contaminants in the fluid can also contaminate the pressure lines leading to erroneous readings. Furthermore, measuring differential pressures nearby the cylinder does not have a unique relationship to Magnus Effect. Any factors that influence the differential pressure distribution in proximity to the cylinder can adversely affect the relationship of the differential pressure to the Magnus force and hence affect measurement accuracy.
Other mass flow measurement techniques involving what might on first impression appear to involve similar or perhaps related functionality, have found favor during the last decade. One such class of devices is that known as Coriolis mass flow metrology. However, on closer inspection, it is clear that the fundamental operating principle known as the xe2x80x9cMagnus Effectxe2x80x9d (and the related Kutta-Joukowski Transformation) is totally different from the xe2x80x9cCoriolis Effectxe2x80x9d implemented in Coriolis flow meters, and has not heretofore been successfully implemented as an accepted mass flow measurement technique. The physical phenomena associated with the xe2x80x9cMagnus Effectxe2x80x9d, and that of the xe2x80x9cCoriolis Effectxe2x80x9d are not related or connected in any manner. The Magnus Effect is a special case of the more general Kutta-Joukowski Transformation, which represents one the fundamental principles of aerodynamic lift, and one to which the Coriolis Effect bears no relationship. Fundamentally, Coriolis mass flow meters require that fluid flow through at least one conduit that is caused to vibrate transversely relative to the direction of fluid flow. By contrast, in using the Magnus Effect to measure flow rate, fluid does not flow through a vibrating conduit. Instead, fluid flows outside of and around a rotating probe. Furthermore, the probe of the Magnus Effect device is clearly not a conduit, as fluid contacts only the probe""s outer surface. The xe2x80x9cMagnus Effectxe2x80x9d describes and explains the force experienced by an object placed in a flowing fluid stream which, when the object is rotated, results in the application thereto of a xe2x80x9cliftxe2x80x9d force that is transverse in direction to both the flowstrearn and the axis of rotation of the object. The operating principles of the prior art Magnus effect devices thus clearly bear no relationship to the xe2x80x9cCoriolis Effectxe2x80x9d, or to Coriolis mass flow meters in general. But just as the Coriolis Effect has met with success in the field of flow measurement, it is believed that the Magnus Effect can likewise find useful application. However, as pointed out above, previous attempts at using the principles of the Magnus Effect to measure mass flow rate have not met with great success. There is thus a need for the development of a fundamentally different and distinctive way to measure mass flow rate using the Magnus Effect in a new and unique manner.
It is therefore a primary objective of the present invention to provide new, improved means to directly measure the true mass flow rate of a fluid independent of the fluid""s physical or chemical properties;
Another objective of this present invention is to provide a means for measuring the true mass flow rate of a gas without having to measure density (or other properties such as temperature and pressure to calculate density) in order to determine mass flow rate by combining density with flow velocity or volumetric flow rate;
Still another objective of the present invention is to provide a means for avoiding the additional substantial cost, complexity, and errors associated with inferring mass flow rate from multi-variable measurement methods; and
Yet another objective of the present invention is to provide a means to measure a fluid""s mass flow rate, flow velocity, fluid density, and viscosity using only one common sensing element. In contrast with Coriolis mass flow meters,
Further objectives of this new technology are:
(1) to provide improved means to measure mass flow rate without directing the fluid through a vibrating tube offering improved safety;
(2) to provide an insertion-style design to permit smaller physical size, reduced complexity, and simpler construction to allow substantial reduction in manufacturing cost and installation expense for application on pipes larger than about 3-6 inches (75 to 150 mm) in diameter; and
(3) to provide improved means to measure the true mass flow rate without using xe2x80x9cby-passxe2x80x9d tubes as used in thermal mass flow meters.
Another objective of the present invention is to provide improved means to measure fluid mass flow rate without using a continuously spinning cylinder which requires a constant speed motor and flexible seals; factors that contribute flow measurement errors and limit performance and usage.
In contrast to the xe2x80x9cclassicalxe2x80x9d Magnus Effect described above, a preferred embodiment of the present invention employs a rotationally oscillating probe attached to a support at one of its ends and adapted for extension into a flow stream. The flowing fluid (liquid or gas) interacts with the probe to produce an oscillatory Magnus lift force distributed along the portion of the probe exposed to the fluid stream. The Magnus lift force is directed substantially perpendicular to the direction of fluid flow and to the axis of the probe. The amplitude of the rotational oscillation can be on the order of several degrees. The fluid mass flow rate relates to the magnitude of the resulting oscillatory force (and circulation xcex93) according to the above equations (1) and (3). The probe has static and dynamic properties analogous to those of a cantilevered beam by virtue of its construction and mounting. The oscillatory force causes the probe to experience an oscillating moment and exhibit dynamic motion (and deflection) related to the fluid""s mass flow rate. Mass flow rate is determined by using known motion-responsive sensor means (contained within the probe) to measure the effects of the oscillating force by, measuring dynamic response characteristics of the probe that relate to (or are proportional to) the magnitude of the force. Electronic circuitry and processor means convert electrical signal(s) from the sensor(s) to a usable mass flow rate value and an electronic output signal proportional to mass flow rate.
Alternative embodiments of the invention employ a probe assembly in various xe2x80x9ctuning forkxe2x80x9d type arrangements. One such embodiment employs a probe assembly comprising a xe2x80x9cconcentric tuning forkxe2x80x9d including two elongated structures, one disposed within the other in a coaxial manner (e.g., concentric cylinders) and mounted to a common support. The xe2x80x9cwettedxe2x80x9d exterior surface of the xe2x80x9couterxe2x80x9d structure comprises the xe2x80x9cflow sensitive elementxe2x80x9d (referred to as the xe2x80x9cFSExe2x80x9d) and the xe2x80x9cinnerxe2x80x9d structure functions, in part, as a dynamic counter-balance and can provide a reference for measuring the relative dynamic response characteristics of the xe2x80x9couterxe2x80x9d structure. Electromagnetic actuator means cause the concentric, coaxial components to twist and oscillate relative to one another in opposing rotational directions about a common longitudinal axis in a manner similar to that of a xe2x80x9crotational tuning forkxe2x80x9d thereby imparting rotational (torsional) oscillation to the probe. This xe2x80x9cconcentric rotational tuning-forkxe2x80x9d configuration allows for vibration cancellation, enhances the xe2x80x9cQxe2x80x9d of the vibrating assembly, and minimizes the electrical power needed to sustain oscillation.
In another alternative embodiment of the invention, a xe2x80x9clinear rotational tuning forkxe2x80x9d is formed by two elongated structure disposed to extend opposite one another in xe2x80x9cmirror imagexe2x80x9d fashion along a common longitudinal axis. One structure comprises the FSE and is intended for insertion into the fluid stream. The opposing structure (intended to be located external to the fluid stream) acts as a dynamic counter-balance and provides a reference for measuring the relative dynamic response characteristics of the FSE. Rotational oscillation is imparted to the FSE and the counter-balance by way of a pair of xe2x80x9cconnecting rodsxe2x80x9d through which the applied rotational excitation is applied. Excitation is provided by actuator means that cause the FSE and counter-balance structures to twist and oscillate relative to one another in opposing rotational directions about their common longitudinal axis as a xe2x80x9clinear rotational tuning forkxe2x80x9d. This xe2x80x9clinear rotational tuning-forkxe2x80x9d configuration allows for vibration cancellation, enhances the xe2x80x9cQxe2x80x9d of the vibrating structure, and minimizes electrical power needed to sustain oscillation.
In another alternative embodiment, an additional sensing means integral to the probe assembly allows determination of the fluid""s flow velocity (based on vortex shedding) independent of mass flow rate and allows determination of fluid density by dividing measured mass flow rate by flow velocity.
Yet another embodiment of the present invention allows determination of fluid viscosity in addition to mass flow rate by monitoring the power required to sustain the rotational excitation at a desired angular amplitude level or rotational velocity.
These and other objectives and advantages of the present invention will become apparent to those skilled in the art after having read the following detailed description of the various embodiments illustrated and included in the following several figures of the drawing.